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A190644
Least number k>1 such that (tau(k-1)+tau(k+1))/tau(k) = n where tau = A000005.
1
6, 34, 39, 7, 11, 19, 29, 41, 79, 71, 179, 199, 181, 239, 883, 419, 701, 839, 881, 1429, 2351, 1259, 1871, 2161, 4049, 3079, 3361, 2521, 6481, 4159, 6299, 5279, 11551, 5039, 20789, 7561, 25919, 10079, 16561, 13441, 38611, 13859, 23761, 21839, 100673, 20161
OFFSET
1,1
MAPLE
with(numtheory):
a:= proc(n) local k;
for k from 2 while (tau(k-1)+tau(k+1)) /tau(k)<>n do od; k
end:
seq(a(n), n=1..50); # Alois P. Heinz, May 19 2011
MATHEMATICA
tau = DivisorSigma[0, #]&;
a[n_] := For[k=2, True, k++, If[(tau[k-1]+tau[k+1])/tau[k]==n, Return[k]]];
Array[a, 50] (* Jean-François Alcover, Mar 27 2017 *)
Module[{nn=300000, tau}, tau=(#[[1]]+#[[3]])/#[[2]]&/@Partition[DivisorSigma[ 0, Range[nn]], 3, 1]; Flatten[Table[Position[tau, n, 1, 1], {n, 50}]]+1] (* Harvey P. Dale, Nov 24 2022 *)
PROG
(Sage)
def A190644(n):
tau = number_of_divisors
return next((k for k in IntegerRange(2, infinity) if tau(k-1)+tau(k+1) == n*tau(k))) # D. S. McNeil, May 19 2011
CROSSREFS
Cf. A000005 (number of divisors of n), A190612.
Sequence in context: A354479 A283232 A375569 * A011798 A222174 A044464
KEYWORD
nonn
AUTHOR
STATUS
approved